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import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np
import logging
import mcubes
from icecream import ic
import pdb
def extract_fields(bound_min, bound_max, resolution, query_func):
N = 64
X = torch.linspace(bound_min[0], bound_max[0], resolution).split(N)
Y = torch.linspace(bound_min[1], bound_max[1], resolution).split(N)
Z = torch.linspace(bound_min[2], bound_max[2], resolution).split(N)
u = np.zeros([resolution, resolution, resolution], dtype=np.float32)
with torch.no_grad():
for xi, xs in enumerate(X):
for yi, ys in enumerate(Y):
for zi, zs in enumerate(Z):
xx, yy, zz = torch.meshgrid(xs, ys, zs)
pts = torch.cat([xx.reshape(-1, 1), yy.reshape(-1, 1), zz.reshape(-1, 1)], dim=-1)
val = query_func(pts.cuda()).reshape(len(xs), len(ys), len(zs)).detach().cpu().numpy()
u[xi * N: xi * N + len(xs), yi * N: yi * N + len(ys), zi * N: zi * N + len(zs)] = val
return u
def extract_geometry(bound_min, bound_max, resolution, threshold, query_func, color_func):
print('threshold: {}'.format(threshold))
u = extract_fields(bound_min, bound_max, resolution, query_func)
vertices, triangles = mcubes.marching_cubes(u, threshold)
b_max_np = bound_max.detach().cpu().numpy()
b_min_np = bound_min.detach().cpu().numpy()
vertices = vertices / (resolution - 1.0) * (b_max_np - b_min_np)[None, :] + b_min_np[None, :]
vertices_color = color_func(vertices)
return vertices, triangles, vertices_color
def sample_pdf(bins, weights, n_samples, det=False):
# This implementation is from NeRF
# Get pdf
device = weights.device
weights = weights + 1e-5 # prevent nans
pdf = weights / torch.sum(weights, -1, keepdim=True)
cdf = torch.cumsum(pdf, -1)
cdf = torch.cat([torch.zeros_like(cdf[..., :1]), cdf], -1)
# Take uniform samples
if det:
u = torch.linspace(0. + 0.5 / n_samples, 1. - 0.5 / n_samples, steps=n_samples).to(device)
u = u.expand(list(cdf.shape[:-1]) + [n_samples])
else:
u = torch.rand(list(cdf.shape[:-1]) + [n_samples]).to(device)
# Invert CDF
u = u.contiguous()
inds = torch.searchsorted(cdf, u, right=True)
below = torch.max(torch.zeros_like(inds - 1).to(device), inds - 1)
above = torch.min((cdf.shape[-1] - 1) * torch.ones_like(inds).to(device), inds)
inds_g = torch.stack([below, above], -1) # (batch, N_samples, 2)
matched_shape = [inds_g.shape[0], inds_g.shape[1], cdf.shape[-1]]
cdf_g = torch.gather(cdf.unsqueeze(1).expand(matched_shape), 2, inds_g)
bins_g = torch.gather(bins.unsqueeze(1).expand(matched_shape), 2, inds_g)
denom = (cdf_g[..., 1] - cdf_g[..., 0])
denom = torch.where(denom < 1e-5, torch.ones_like(denom).to(device), denom)
t = (u - cdf_g[..., 0]) / denom
samples = bins_g[..., 0] + t * (bins_g[..., 1] - bins_g[..., 0])
return samples
class NeuSRenderer:
def __init__(self,
nerf,
sdf_network,
deviation_network,
color_network,
n_samples,
n_importance,
n_outside,
up_sample_steps,
perturb,
sdf_decay_param):
self.nerf = nerf
self.sdf_network = sdf_network
self.deviation_network = deviation_network
self.color_network = color_network
self.n_samples = n_samples
self.n_importance = n_importance
self.n_outside = n_outside
self.up_sample_steps = up_sample_steps
self.perturb = perturb
self.sdf_decay_param = sdf_decay_param
def render_core_outside(self, rays_o, rays_d, z_vals, sample_dist, nerf, background_rgb=None):
"""
Render background
"""
batch_size, n_samples = z_vals.shape
# Section length
dists = z_vals[..., 1:] - z_vals[..., :-1]
dists = torch.cat([dists, torch.Tensor([sample_dist]).expand(dists[..., :1].shape)], -1)
mid_z_vals = z_vals + dists * 0.5
# Section midpoints
pts = rays_o[:, None, :] + rays_d[:, None, :] * mid_z_vals[..., :, None] # batch_size, n_samples, 3
dis_to_center = torch.linalg.norm(pts, ord=2, dim=-1, keepdim=True).clip(1.0, 1e10)
pts = torch.cat([pts / dis_to_center, 1.0 / dis_to_center], dim=-1) # batch_size, n_samples, 4
dirs = rays_d[:, None, :].expand(batch_size, n_samples, 3)
pts = pts.reshape(-1, 3 + int(self.n_outside > 0))
dirs = dirs.reshape(-1, 3)
density, sampled_color = nerf(pts, dirs)
sampled_color = torch.sigmoid(sampled_color)
alpha = 1.0 - torch.exp(-F.softplus(density.reshape(batch_size, n_samples)) * dists)
alpha = alpha.reshape(batch_size, n_samples)
weights = alpha * torch.cumprod(torch.cat([torch.ones([batch_size, 1]), 1. - alpha + 1e-7], -1), -1)[:, :-1]
sampled_color = sampled_color.reshape(batch_size, n_samples, 3)
color = (weights[:, :, None] * sampled_color).sum(dim=1)
if background_rgb is not None:
color = color + background_rgb * (1.0 - weights.sum(dim=-1, keepdim=True))
return {
'color': color,
'sampled_color': sampled_color,
'alpha': alpha,
'weights': weights,
}
def up_sample(self, rays_o, rays_d, z_vals, sdf, n_importance, inv_s):
"""
Up sampling give a fixed inv_s
"""
device = rays_o.device
batch_size, n_samples = z_vals.shape
pts = rays_o[:, None, :] + rays_d[:, None, :] * z_vals[..., :, None] # n_rays, n_samples, 3
radius = torch.linalg.norm(pts, ord=2, dim=-1, keepdim=False)
inside_sphere = (radius[:, :-1] < 1.0) | (radius[:, 1:] < 1.0)
sdf = sdf.reshape(batch_size, n_samples)
prev_sdf, next_sdf = sdf[:, :-1], sdf[:, 1:]
prev_z_vals, next_z_vals = z_vals[:, :-1], z_vals[:, 1:]
mid_sdf = (prev_sdf + next_sdf) * 0.5
cos_val = (next_sdf - prev_sdf) / (next_z_vals - prev_z_vals + 1e-5)
# ----------------------------------------------------------------------------------------------------------
# Use min value of [ cos, prev_cos ]
# Though it makes the sampling (not rendering) a little bit biased, this strategy can make the sampling more
# robust when meeting situations like below:
#
# SDF
# ^
# |\ -----x----...
# | \ /
# | x x
# |---\----/-------------> 0 level
# | \ /
# | \/
# |
# ----------------------------------------------------------------------------------------------------------
prev_cos_val = torch.cat([torch.zeros([batch_size, 1]).to(device), cos_val[:, :-1]], dim=-1)
cos_val = torch.stack([prev_cos_val, cos_val], dim=-1)
cos_val, _ = torch.min(cos_val, dim=-1, keepdim=False)
cos_val = cos_val.clip(-1e3, 0.0) * inside_sphere
dist = (next_z_vals - prev_z_vals)
prev_esti_sdf = mid_sdf - cos_val * dist * 0.5
next_esti_sdf = mid_sdf + cos_val * dist * 0.5
prev_cdf = torch.sigmoid(prev_esti_sdf * inv_s)
next_cdf = torch.sigmoid(next_esti_sdf * inv_s)
alpha = (prev_cdf - next_cdf + 1e-5) / (prev_cdf + 1e-5)
weights = alpha * torch.cumprod(
torch.cat([torch.ones([batch_size, 1]).to(device), 1. - alpha + 1e-7], -1), -1)[:, :-1]
z_samples = sample_pdf(z_vals, weights, n_importance, det=True).detach()
return z_samples
def cat_z_vals(self, rays_o, rays_d, z_vals, new_z_vals, sdf, last=False):
batch_size, n_samples = z_vals.shape
_, n_importance = new_z_vals.shape
pts = rays_o[:, None, :] + rays_d[:, None, :] * new_z_vals[..., :, None]
z_vals = torch.cat([z_vals, new_z_vals], dim=-1)
z_vals, index = torch.sort(z_vals, dim=-1)
if not last:
new_sdf = self.sdf_network.sdf(pts.reshape(-1, 3)).reshape(batch_size, n_importance)
sdf = torch.cat([sdf, new_sdf], dim=-1)
xx = torch.arange(batch_size)[:, None].expand(batch_size, n_samples + n_importance).reshape(-1)
index = index.reshape(-1)
sdf = sdf[(xx, index)].reshape(batch_size, n_samples + n_importance)
return z_vals, sdf
def render_core(self,
rays_o,
rays_d,
z_vals,
sample_dist,
sdf_network,
deviation_network,
color_network,
background_alpha=None,
background_sampled_color=None,
background_rgb=None,
cos_anneal_ratio=0.0):
batch_size, n_samples = z_vals.shape
device = rays_o.device
# Section length
dists = z_vals[..., 1:] - z_vals[..., :-1]
dists = torch.cat([dists, torch.Tensor([sample_dist]).expand(dists[..., :1].shape).to(device)], -1)
mid_z_vals = z_vals + dists * 0.5
# Section midpoints
pts = rays_o[:, None, :] + rays_d[:, None, :] * mid_z_vals[..., :, None] # n_rays, n_samples, 3
dirs = rays_d[:, None, :].expand(pts.shape)
pts = pts.reshape(-1, 3)
dirs = dirs.reshape(-1, 3)
sdf_nn_output = sdf_network(pts)
sdf = sdf_nn_output[:, :1]
feature_vector = sdf_nn_output[:, 1:]
gradients = sdf_network.gradient(pts).squeeze()
sampled_color = color_network(pts, gradients, dirs, feature_vector).reshape(batch_size, n_samples, 3)
inv_s = deviation_network(torch.zeros([1, 3]).to(device))[:, :1].clip(1e-6, 1e6) # Single parameter
inv_s = inv_s.expand(batch_size * n_samples, 1)
true_cos = (dirs * gradients).sum(-1, keepdim=True)
# "cos_anneal_ratio" grows from 0 to 1 in the beginning training iterations. The anneal strategy below makes
# the cos value "not dead" at the beginning training iterations, for better convergence.
iter_cos = -(F.relu(-true_cos * 0.5 + 0.5) * (1.0 - cos_anneal_ratio) +
F.relu(-true_cos) * cos_anneal_ratio) # always non-positive
# Estimate signed distances at section points
estimated_next_sdf = sdf + iter_cos * dists.reshape(-1, 1) * 0.5
estimated_prev_sdf = sdf - iter_cos * dists.reshape(-1, 1) * 0.5
prev_cdf = torch.sigmoid(estimated_prev_sdf * inv_s)
next_cdf = torch.sigmoid(estimated_next_sdf * inv_s)
p = prev_cdf - next_cdf
c = prev_cdf
alpha = ((p + 1e-5) / (c + 1e-5)).reshape(batch_size, n_samples).clip(0.0, 1.0)
pts_norm = torch.linalg.norm(pts, ord=2, dim=-1, keepdim=True).reshape(batch_size, n_samples)
inside_sphere = (pts_norm < 1.0).float().detach()
relax_inside_sphere = (pts_norm < 1.2).float().detach()
# Render with background
if background_alpha is not None:
alpha = alpha * inside_sphere + background_alpha[:, :n_samples] * (1.0 - inside_sphere)
alpha = torch.cat([alpha, background_alpha[:, n_samples:]], dim=-1)
sampled_color = sampled_color * inside_sphere[:, :, None] +\
background_sampled_color[:, :n_samples] * (1.0 - inside_sphere)[:, :, None]
sampled_color = torch.cat([sampled_color, background_sampled_color[:, n_samples:]], dim=1)
weights = alpha * torch.cumprod(torch.cat([torch.ones([batch_size, 1]).to(device), 1. - alpha + 1e-7], -1), -1)[:, :-1]
weights_sum = weights.sum(dim=-1, keepdim=True)
color = (sampled_color * weights[:, :, None]).sum(dim=1)
if background_rgb is not None: # Fixed background, usually black
color = color + background_rgb.to(device) * (1.0 - weights_sum)
# Eikonal loss
gradient_error = (torch.linalg.norm(gradients.reshape(batch_size, n_samples, 3), ord=2,
dim=-1) - 1.0) ** 2
gradient_error = (relax_inside_sphere * gradient_error).sum() / (relax_inside_sphere.sum() + 1e-5)
depth = (mid_z_vals * weights[:, :n_samples]).sum(dim=1, keepdim=True)
return {
'color': color,
'sdf': sdf,
'dists': dists,
'gradients': gradients.reshape(batch_size, n_samples, 3),
's_val': 1.0 / inv_s,
'mid_z_vals': mid_z_vals,
'weights': weights,
'cdf': c.reshape(batch_size, n_samples),
'gradient_error': gradient_error,
'inside_sphere': inside_sphere,
'depth': depth,
}
def render(self, rays_o, rays_d, near, far, perturb_overwrite=-1, background_rgb=None, cos_anneal_ratio=0.0):
batch_size = len(rays_o)
device = rays_o.device
sample_dist = 2.0 / self.n_samples # Assuming the region of interest is a unit sphere
z_vals = torch.linspace(0.0, 1.0, self.n_samples)
z_vals = near + (far - near) * z_vals[None, :]
z_vals_outside = None
if self.n_outside > 0:
z_vals_outside = torch.linspace(1e-3, 1.0 - 1.0 / (self.n_outside + 1.0), self.n_outside)
n_samples = self.n_samples
perturb = self.perturb
if perturb_overwrite >= 0:
perturb = perturb_overwrite
if perturb > 0:
t_rand = (torch.rand([batch_size, 1]) - 0.5)
z_vals = z_vals + t_rand * 2.0 / self.n_samples
z_vals = z_vals.to(device)
if self.n_outside > 0:
mids = .5 * (z_vals_outside[..., 1:] + z_vals_outside[..., :-1])
upper = torch.cat([mids, z_vals_outside[..., -1:]], -1)
lower = torch.cat([z_vals_outside[..., :1], mids], -1)
t_rand = torch.rand([batch_size, z_vals_outside.shape[-1]])
z_vals_outside = lower[None, :] + (upper - lower)[None, :] * t_rand
if self.n_outside > 0:
z_vals_outside = far / torch.flip(z_vals_outside, dims=[-1]) + 1.0 / self.n_samples
background_alpha = None
background_sampled_color = None
# Up sample
if self.n_importance > 0:
with torch.no_grad():
pts = rays_o[:, None, :] + rays_d[:, None, :] * z_vals[..., :, None]
sdf = self.sdf_network.sdf(pts.reshape(-1, 3)).reshape(batch_size, self.n_samples)
for i in range(self.up_sample_steps):
new_z_vals = self.up_sample(rays_o,
rays_d,
z_vals,
sdf,
self.n_importance // self.up_sample_steps,
64 * 2**i)
z_vals, sdf = self.cat_z_vals(rays_o,
rays_d,
z_vals,
new_z_vals,
sdf,
last=(i + 1 == self.up_sample_steps))
n_samples = self.n_samples + self.n_importance
# Background model
if self.n_outside > 0:
z_vals_feed = torch.cat([z_vals, z_vals_outside], dim=-1)
z_vals_feed, _ = torch.sort(z_vals_feed, dim=-1)
ret_outside = self.render_core_outside(rays_o, rays_d, z_vals_feed, sample_dist, self.nerf)
background_sampled_color = ret_outside['sampled_color']
background_alpha = ret_outside['alpha']
# Render core
ret_fine = self.render_core(rays_o,
rays_d,
z_vals,
sample_dist,
self.sdf_network,
self.deviation_network,
self.color_network,
background_rgb=background_rgb,
background_alpha=background_alpha,
background_sampled_color=background_sampled_color,
cos_anneal_ratio=cos_anneal_ratio)
color_fine = ret_fine['color']
weights = ret_fine['weights']
weights_sum = weights.sum(dim=-1, keepdim=True)
gradients = ret_fine['gradients']
s_val = ret_fine['s_val'].reshape(batch_size, n_samples).mean(dim=-1, keepdim=True)
# - randomly sample points from the volume, and maximize the sdf
pts_random = torch.rand([1024, 3]).float().cuda() * 2 - 1 # normalized to (-1, 1)
sdf_random = self.sdf_network(pts_random)[:, :1]
sparse_loss_1 = torch.exp(
-1 * torch.abs(sdf_random) * self.sdf_decay_param).mean() # - should equal
sparse_loss_2 = torch.exp(-1 * torch.abs(ret_fine['sdf']) * self.sdf_decay_param).mean()
sparse_loss = (sparse_loss_1 + sparse_loss_2) / 2
return {
'color_fine': color_fine,
'depth': ret_fine['depth'],
's_val': s_val,
'sparse_loss': sparse_loss,
'cdf_fine': ret_fine['cdf'],
'weight_sum': weights_sum,
'weight_max': torch.max(weights, dim=-1, keepdim=True)[0],
'gradients': gradients,
'weights': weights,
'gradient_error': ret_fine['gradient_error'],
'inside_sphere': ret_fine['inside_sphere']
}
def get_vertex_colors(self, vertices):
"""
@param vertices: n,3
@return:
"""
V = vertices.shape[0]
bn = 20480
verts_colors = []
with torch.no_grad():
for vi in range(0, V, bn):
verts = torch.from_numpy(vertices[vi:vi+bn].astype(np.float32)).cuda()
feats = self.sdf_network(verts)[..., 1:]
# pdb.set_trace()
gradients = self.sdf_network.gradient(verts) # ...,3
gradients = F.normalize(gradients, dim=-1).squeeze(1)
# pdb.set_trace()
colors = self.color_network(verts, gradients, gradients, feats)
colors = torch.clamp(colors,min=0,max=1).cpu().numpy()
verts_colors.append(colors)
verts_colors = (np.concatenate(verts_colors, 0)*255).astype(np.uint8)
return verts_colors[:, ::-1]
def extract_geometry(self, bound_min, bound_max, resolution, threshold=0.0):
return extract_geometry(bound_min,
bound_max,
resolution=resolution,
threshold=threshold,
query_func=lambda pts: -self.sdf_network.sdf(pts),
color_func=lambda pts: self.get_vertex_colors(pts))
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